Question

$5,000 is deposited today into a bank account. The account earns 3.2% per annum compounded half yearly for the first 7 years, then 8.2% per annum compounded quarterly thereafter. Assuming no further deposits or withdrawals are made, (d) Calculate the account balance 10 years from today.

A loan of $100,000 is made today. The borrower will make equal repayments of $3800.75 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown). For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage: (a) The loan is fully repaid exactly after 31 monthly repayments, i.e., the loan outstanding immediately after 31 repayments is exactly 0.

A loan of $100,000 is made today. The borrower will make equal repayments of $3800.75 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown). For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage: (b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $26281.16.

Answer 1

Effective half-yearly rate = 3.2%/2 = 1.6%

There are 14 half-year periods in the first 7 years.

The future value of $5,000 in year 7 = 5,000 * (1 + 0.016)^14 = $6,244.2734805072

Effective quarterly rate = 8.2%/4 = 2.05%

There are 12 quarters in 3 years form year 8 to year year 10.

The future value of $6,244.2734805072 in year 10 = 6,244.2734805072*(1 + 0.0205)^12 = $7,965.9582190439

The amount balance 10 years from now = $7,965.9582190439

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